MinT - Information on Result #1840431

Information on Result #1840431

(66, 81, 299595)-net in base 16, using net defined by OOA based on OOA(16⁸¹, 299595, S₁₆, 15, 15), using

OOA 7-folding and stacking with additional row [i] based on OA(16⁸¹, 2097166, S₁₆, 15), using
- discarding factors based on OA(16⁸¹, 2097168, S₁₆, 15), using
  - discarding parts of the base [i] based on linear OA(128⁴⁶, 2097168, F₁₂₈, 15) (dual of [2097168, 2097122, 16]-code), using
    - constructionÂ X applied to C([0,7]) âŠ‚ C([0,5]) [i] based on
      1. linear OA(128⁴³, 2097153, F₁₂₈, 15) (dual of [2097153, 2097110, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
      2. linear OA(128³¹, 2097153, F₁₂₈, 11) (dual of [2097153, 2097122, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
      3. linear OA(128³, 15, F₁₂₈, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,128) or 15-cap in PG(2,128)), using
        discarding factors / shortening the dual code based on linear OA(128³, 128, F₁₂₈, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
        Reedâ€“Solomon code RS(125,128) [i]

Mode: Constructive.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	(67, 82, 299595)-net in base 16	[i]		Net Duplication